Contrary to what some politicians like to claim, not every right automatically implies a balancing responsibility or restraint. But a newspaper's right to publish, including the right to report what is said in parliament, hard won in the 18th century, is one that does. The right to tell the reader what has happened and has been said is balanced by a duty to tell the truth, to respect others and to act within the law. That is why the naming of Ryan Giggs by the MP John Hemming this week, in defiance of an injunction that is still in force, poses such difficult questions for the media and for the constitution.

MPs' and peers' protection under parliamentary privilege to say anything they choose is undoubtedly another such right. Privilege is absolutely the right word for this formidable constitutional protection, which dates from the time when parliament was the nation's frontline of defence against the authority of the church and the king. Yet in an era in which neither the church nor the crown poses such a challenge, new assumptions perhaps apply. As the select committee on parliamentary privilege put it 12 years ago: "Free speech is the most important parliamentary privilege and members should be careful not to abuse it."

Views differ as to whether Mr Hemming – or Lord Stoneham in the Lords last week – abused that right. The argument is not open and shut. And it is certainly not restricted to the issue of privacy injunctions. The case also raises further questions that have not been tested in modern times. When parliament last looked in depth at the issue of privilege, its main concerns were over MPs who might make statements on sub judice issues and on national security. Yet what would happen if a newspaper persuaded an MP to act as a mouthpiece to make otherwise defamatory claims about individuals in the public eye, then broadcast them through social media, in order that those claims – whether true or not – could then be reported in the newspapers and by broadcasters? It is not an altogether fanciful scenario and it is doubtful whether the Speaker could stop it, even if he wanted to. A retrospective suspension, even if MPs backed it, would be the equivalent of shutting the stable door after the horse has bolted.

When parliament last examined the question of privilege, the internet was still in its infancy. Social media were embryonic. And the ink on the Human Rights Act was barely dry. The possibility that parliamentary privilege might intersect with the online world and the role of the press in all its complexity was not even imagined. At the very least, a new select committee examination is now required. And so, inescapably, are some clearer new responsibilities to go with MPs' ancient rights.